Finite Group DatabasebetaFinite Group Databasebeta| order | 10016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14578818 |
| unambiguous semidirect product | (C2×#14578818)⋊C2 |
| Fitting | C22×C313 ⋊ C8 |
| Sylow | C313 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,313|a^2=d,d^2=e,b^a=bc,f^a=f^5,f^d=f^25,f^e=f^312176 conjugacy classes — view the full character table.
| maximal subgroup of | #34095237, #34095238, C2×C22⋊#14578818, … |
| maximal normal subgroup of | #34095237, #34095238, C2×C22⋊#14578818, … |
| maximal quotient of | #34095237, #34095238, D4⋊#14578818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10016, 238);